Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
How will you work out which numbers have been used to create this multiplication square?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
A number game requiring a strategy.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Choose a symbol to put into the number sentence.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What is happening at each box in these machines?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
How would you find out how many football cards Catrina has collected?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Are you resilient enough to solve these number problems?
This task combines spatial awareness with addition and multiplication.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This problem looks at how one example of your choice can show something about the general structure of multiplication.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
An old game but lots of arithmetic!
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.